Question

You have gathered information about the expected returns and standard deviations of two stocks, which is given in the table below:

	Expected return	Standard deviation
Bull Inc	10.0%	30.0%
Bear Inc	6.0%	20.0%

a. Discuss which stock is more attractive and why? (hint: think about the assumptions first)

You are going to form a portfolio, which includes these two stocks. The value of your total portfolio is 800 000 and investment into stock B is 60% of the total portfolio.

b. It is estimated that the correlation between the stock returns is -0.50. Explain, what does this result mean?

c. Calculate the portfolio risk and expected return, and explain the benefits of diversification.

(Show your work, you may upload the solution file)

Answer 1

a. Risk and returns are inversely proportional to each other. Choice of stock depends upon the risk taking capacity of an investor. Bull Inc is giving return of 10% which is higher than return on Bear Inc. Also the risk is high in Bull Inc. The risk averse investor who is reluctant to take should go for Bear Inc. While risk seeking investor may opt for Bull Inc as he has more potential to take risk. In case portfolio will be framed, 4,80,000 will be invested in Bear Inc and 2,40,000 will be invested in Bull Inc.

b. Correlation between stock returns signifies degree of relationship between price variations of different stocks in a portfolio. Negative correlation means price moves in opposite direction. Borrelation of -0.50 means, as the price of one stock will increase, the price of other stock will decrease proportionally by 0.50 times.

Expected return of portfolio= Return of A *Weight of A +Return of B*Weight of B

=10*0.40+6*0.60 = 7.6%

p=square root of (w₁²₁²+w₂²₂²+2w₁w₂cov_1,2)

cov_1,2= cor_{1,2 *12}

=0.40*0.4*0.30*0.30+0.60*0.60*0.20*0.20+2*0.40*0.60*(0.50)*0.3*0.20

=0.12

This truely reflects the benefit of diversification. As the risk of portfolio has been decreased as compare to the individual risk of portfolios.